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Advance Math Series 2000 Important Questions Mensuration Part 14

Advance Math Series 2000 Important Questions Mensuration Part 14

Advance Math Series 2000 Important Questions Mensuration Part 14

Q1042. A copper wire of length 36 m and diameter 2 mm is melted to form a sphere. The radius of the sphere (in cm) is

(a) 2.5                                   (b) 3                                       (c) 3.5                                    (d) 4

Q1043.A child reshapes a cone made up of clay of height 24cm and radius 6 cm into a sphere. The radius (in cm) of the sphere is

(a) 6                                       (b) 12                                    (c) 24                                     (d) 48

Q1044. The total surface area of a solid right circular cylinder is twice that of a solid sphere. If they have the same radii, the ratio of the volume of the cylinder to that of the sphere is given by

(a) 9 : 4                                 (b) 2 : 1                                 (c) 3 : 1                                  (d) 4 : 9

Q1045. Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10m and depth 2m. In how much time will the cistern be filled?

(a) 1 hour       (b) 1 hour 40 minutes     (c) 1 hour 20 minutes     (d) 2 hours 40 minutes

Advance Math Series
Q1046.Marbles of diameter 1.4 cm are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it, if the water rises by 5.6 cm.

(a) 50                                     (b) 150                                  (c) 250                                   (d) 350

Q1047.A solid metallic sphere of radius 8 cm is melted to form 64 equal small solid spheres. The ratio of the surface area of this sphere to that of a small sphere is

(a) 4 : 1                                 (b) 1 : 16                               (c) 16 : 1                               (d) 1 : 4

Q1048.The areas of three consecutive faces of a cuboid are 12 cm2, 20 cm2 and 15 cm2, then the volume (in cm3) of the cuboid is

(a) 3600                                (b) 100                                  (c) 80                                     (d) 60

Q1049.The sides of a triangle are in the ratio 2 : 3 : 4. The perimeter of the triangle is 18 cm. The area (in cm2) of the triangle is

(a) 9                                       (b) 36                                    (c)                                  (d) 3

Q1050.if a wire is bent into the shape of a square, then the area of the, square so formed is 81 cm2. When the wire is rebent into a semicircular shape, then the area. (in cm2) of the semi circle will be(Take π =22/7)

(a) 22                                     (b) 44                                    (c) 77                                     (d) 154

Q1051.If the radius of a circle is increased by 50%, its area is increased by

(a) 125%                               (b) 100%                              (c) 75%                                 (d) 50%

Q1052.A hemisphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surfaces will be

(a) 1 :√2                               (b) √2 : 1                             (c) 1 : 2                                  (d) 2 : 1

Q1053.The floor of a room is of size 4m × 3m  and its height is 3m. The walls and ceiling of the room require painting. The area to be painted is

(a) 66m2                               (b) 54m2                               (c) 43m2                               (d) 33m2

Q1054.In an equilateral triangle ABC of side 10 cm, the side BC is trisected at D, Then the length (in cm) of AD is

(a) 3√3                                 (b) 7√3                             (c) 10√7/3                           (d)7√10/3

Q1055. Water is flowing at the rate of 5 km/h through a pipe of diameter 14 cm into a rectangular tank which is 50 m long, 44m wide. The time taken, in hours, for the rise in the level of water in the tank to be 7 cm is

(a) 2                                       (b)5/2                                    (c) 3                                       (d) 5/2

Q1056. The side of a quadrilateral are in the ratio 3 : 4 : 5 : 6 and its perimeter is 72 cm. The length of its greatest side (in cm) is

(a) 24                                     (b) 27                                    (c) 30                                     (d) 36

Q1057. The volume (in cm3) of rain water that can be collected from 1.5 hectares of ground in a rainfall of 5 cm is

(a) 75                                     (b) 750                                  (c) 7500                                (d) 75000

Q1058. A drum of kerosene is 3/4full. When 30 litres of kerosene is drawn from it, it remains 7/12 full. The capacity of the drum is

(a) 120 ?                                (b) 135 ?                               (c) 150 ?                                (d) 180 ?

Q1059. The length (in cm) of a chord of a circle of radius 13 cm at a distance of 12 cm from its centre is

(a) 5                                       (b) 8                                       (c) 10                                     (d) 12

Q1060. A copper wire is bent in the form of square with an area of 121 cm2. If the same wire is bent in the form of a circle, the radius (in cm) of the circle is(Take π = 22/7)

(a) 7                                       (b) 10                                    (c) 11                                     (d) 14

Q1061. A copper wire is bent in the form of an equilateral triangle and has area 121√3 cm2. If the same wire is bent into the form of a circle, the area (in cm2) enclosed by the wire is(Take π = 22/7)

(a) 364.5                               (b) 693.5                              (c) 346.5                               (d) 639.5

Q1062. If the length of a rectangular plot of land is increased by 5% and the breadth is decreased by 10%, how much will its area increase or decrease?

(a) 6.5% increase              (b) 5.5% decrease            (c) 5.5% increase              (d) 6.5% decrease

Q1063. The radius of base and slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 cm2, then the radius (in cm) of its base is (Use  π= 22/7)

(a) 8                                       (b) 12                                    (c) 14                                     (d) 16

Q1064. The area of a right-angled isosceles triangle having hypotenuse 16 cm is

(a) 144 cm2                          (b) 128 cm2                         (c) 112 cm2                          (d) 110 cm2

Q1065. The ratio of the radii of two wheels is 3 : 4. The ratio of their circumferences is

(a) 4 : 3                                 (b) 3 : 4                                 (c) 2 : 3                                  (d) 3 : 2

Q1066. A right circular cylinder just encloses a sphere of radius r. The ratio of the surface area of the sphere and the curved surface area of the cylinder is

(a) 2 : 1                                 (b) 1 : 2                                 (c) 1 : 3                                  (d) 1 : 1

Advance Math Series
Q1067. If each of the radius of base and height of a right circular cone is increased by 10%, then the percentage of increase in the volume of the cone will be

(a) 20                                     (b) 33.1                                 (c) 44.2                                 (d) 100

Q1068. The ratio of the areas of two isosceles triangles having equal vertical angles is 1: 4. The ratio of their heights will be

(a) 1 : 2                                 (b) 3 : 4                                 (c) 2 : 3                                  (d)   6 : 7

Q1069. The area of an equilateral triangle, inscribed in a circle, is 4√3 cm2. The area of the circle is terms of π will be

(a) 4√6 π                        (b) 5π                               (c) 5 1/3π                                    (d) 6π

Q1070. If each side of a square is increased by 10% what is the percentage of increase of the area?

(a) 10                             (b) 21                                 (c) 42                                 (d) 100

Q1071. If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, the change in its area will be

(a) 1% increase                 (b) 1% decrease                        (c) 10% increase               (d) No change

Q1072. Two solid cylinders of radii 4 cm and 5cm and lengths 6 cm and 4cm respectively are recast into cylindrical disc of thickness 1 cm. The radius of the disc is

(a) 7 cm                                   (b) 14 cm                            (c) 21 cm                            (d) 28 cm

Q1073. An equilateral triangle of side 6 cm has its corners cut off to form a regular hexagon. Area (in cm2) of his regular hexagon will be

(a) 3√3                                 (b) 3 √6                                (c) 6√3                                 (d)5√3/2

Q1074. The largest sphere is carved out of cube of side 7 cm. The volume of the sphere (in cm3) will be

(a) 718.66                            (b) 543.72                            (c) 481.34                             (d) 179.67

Q1075. If each side of a square is increased by 10%, its area will be increased by

(a) 10%                                 (b) 21%                                 (c) 44%                                 (d) 100%

Q1076. If the circumference of a circle is decreased by 50% then the percentage of decrease in its area is

(a) 25                                     (b) 50                                    (c) 60                                     (d) 75

Q1077.The length (in metres) of the longest rod that can be put in a room of dimensions 10 m × 10 m×10m×5m is

(a) 15√3                               (b) 15                                    (c) 10√2                               (d) 5√3

Q1078. What part of a ditch, 48 metres long 16.5 metres broad and 4 metres deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 metres and length 56 metres?(

(a)  1/9                              (b) 2/9                                 (c)7/9                                  (d)8/9

Q1079. Volume of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5. The ratio of their heights is

(a) 1 : 5                                 (b) 5 : 4                                 (c) 5 : 16                               (d) 25 : 64

Q1080. The radius of circle A is twice that of circle B and the radius of circle B is twice that of circle C. Their area will be in the ratio

(a) 16 : 4 : 1                         (b) 4 : 2 : 1                           (c) 1 : 2 : 4                            (d) 1 : 4 : 16

Q1081. The sides of a triangle are 6 cm, 8 cm and 10 cm. The area of the greatest square that can be inscribed in it, is

(a) 18 cm2                          (b) 15 cm2                        (c) 2304/49 cm2                      (d)576/50  cm2

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